{"paper":{"title":"Weights of reasonable growth and their application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mateusz Krukowski","submitted_at":"2017-09-01T16:03:02Z","abstract_excerpt":"In the paper, we introduce the concept of weight with reasonable growth on a locally compact group $G$. We verify that these weights form a natural class to work with, by examining the most common examples. We proceed with the discussion of the $L^p-$conjecture. With the use of Riesz-Thorin-Stein-Weiss interpolation, we establish that \\mbox{$L^p_{\\omega}(G)\\star L^p_{\\omega}(G)\\subset L^p_{\\omega}(G)$}, $p>1$ implies that $L^p_{\\omega}(G)\\star L^q_{\\omega}(G)\\subset L^q_{\\omega}(G)$ for $q$ which lies between $p$ and $p'$. At last, we confirm the $L^p_{\\omega}-$conjecture for weights of $(p,q)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00380","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}